Fast-Scale and Slow-Scale Subharmonic Oscillation of Valley Current-Mode Controlled Buck Converter

A valley current-mode （VCM） controfled buck converter with current source load （CSI） has complex phenomena of fast-scale and slow-scale subharmonic oscillations. The piecewise smooth switching model of the VCM controlled buck converter with CSI is established. It is found that attractive regions of fast-scale and slow-scale subharmonic oscillations exist in the bifurcation diagram, and two tori exist in the corresponding Poincare mapping. The research results by time-domain simulation indicate that U-type subharmonic oscillation （SO） constituted by SO and frequency-reduced subharmonic oscillation （FSO） exists in inductor current, and sine-type SO constituted by fast scale and low scale exists in output voltage respectively. Experimental results are given to verify the analysis and simulation results.     

Non-Smooth Bifurcation and Chaos in a DC-DC Buck Converter

A direct-current-direct-current （DC-DC） buck converter with integrated load current feedback is studied with three kinds of Poincaré maps. The external corner-collision bifurcation occurs when the crossing number per period varies, and the internal corner-collision bifurcations occur along with period-doubling and period-tripling bifurcations in this model. The multi-band chaos roots in external corner-collision bifurcation and often grows into 1-band chaos. A new kind of chaotic sliding orbits, which is more complex for non-smooth systems, is also found in this model.     

基于比例积分控制的电压反馈型Buck变换器分岔

在分段光滑模型的基础上,推导出基于比例积分(PI)控制的电压反馈型Buck变换器的光滑模型及离散迭代模型.证明了功率系统的混沌吸引子在负载线上运动,并受到占空比的控制,模型的流形围绕吸引子运动并出现1周期、2周期及混沌现象;推导出电压反馈型PI控制系统的输出电压与Buck变换器的输出电压成线性关系,在此基础上指出PI控制中的比例因子起主导作用;分析了系统的倍周期分岔、边界碰撞和混沌现象,并展示了变换器状态的转移过程.实验结果表明了理论建模分析和仿真的正确性.     

基于交错Buck变换器的光伏系统MPPT控制

具有最大功率点跟踪(MPPT)功能的控制器常采用单相Buck变换器,输出功率稳定性差。鉴于此,提出将交错并联技术应用于Buck变换器,并以两相交错并联Buck变换器为例进行研究,减小输出电压、电流纹波,提高了输出功率稳定性,有利于实现MPPT控制;然后针对固定步长扰动观察法跟踪速度与精度之间的矛盾,研究了一种自适应变步长的算法,MATLAB仿真结果表明,改进算法具有较好的跟踪速度和稳态性能。     

Dynamic Feedback Controlling Chaos in Current-Mode Boost Converter

A method for the control of chaos in the current-mode boost converter is presented by using the first-order dynamic feedback control. The feedback part consists of a resistance and a capacitance in series. The system to be controlled is treated as a third-order model, and then the discrete mapping model is obtained by using the data-sampling method. By analysing the position of the maximum norm eigenvalue, the stable range of feedback gain is ascertained out and its optimization is also carried out. Finally, the results of simulation and experiment confirm the correctness of the theoretical analysis and the validity of the proposed means.     

Chaos control via TDFC in time-delayed systems: The harmonic balance approach

This Letter deals with the problem of designing time-delayed feedback controllers (TDFCs) to stabilize unstable equilibrium points and periodic orbits for a class of continuous time-delayed chaotic systems. Harmonic balance approach is used to select the appropriate controller parameters: delay time and feedback gain. The established theoretical results are illustrated via a case study of the well-known Logistic model.     

Bifurcation and chaos in high-frequency peak current mode Buck converter

Bifurcation and chaos in high-frequency peak current mode Buck converter working in continuous conduction mode(CCM) are studied in this paper. First of all, the two-dimensional discrete mapping model is established. Next, reference current at the period-doubling point and the border of inductor current are derived. Then, the bifurcation diagrams are drawn with the aid of MATLAB. Meanwhile, circuit simulations are executed with PSIM, and time domain waveforms as well as phase portraits in i_L–v_C plane are plotted with MATLAB on the basis of simulation data. After that, we construct the Jacobian matrix and analyze the stability of the system based on the roots of characteristic equations. Finally, the validity of theoretical analysis has been verified by circuit testing. The simulation and experimental results show that,with the increase of reference current I_(ref), the corresponding switching frequency f is approaching to low-frequency stage continuously when the period-doubling bifurcation happens, leading to the converter tending to be unstable. With the increase of f, the corresponding Irefdecreases when the period-doubling bifurcation occurs, indicating the stable working range of the system becomes smaller.     

Hopf Bifurcation Control of a Hyperchaotic Circuit System

This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system. The stability of the hyperchaotie circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. An important feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions.     

Hopf Bifurcation Control of a Hyperchaotic Circuit System

This paper is concerned with the Hopf bifurcation control of a newhyperchaotic circuit system. The stability of the hyperchaotic circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. Animportant feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions.     

Self-Stable Chaos Control of dc-dc Converter

A new concept related to self-stable chaos control is first put forward, and its theoretical basis and realization are presented from the frequency-domain perspective. With a new analogous-circuit realization of this control its applications in the voltage-mode Buck converter is discussed. The harmonic-balance method is applied to determine the control range of the control parameter. The experiment results given in the last part confirm the validity of the proposed control method.     

Bifurcation analysis of the logistic map via two periodic impulsive forces

The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.     

Control of Codimension-2 Bautin Bifurcation in Chaotic Lu System

In this paper, we design a feedback controller, and analytically determine a control criterion so as to control the codimension-2 Bautin bifurcation in the chaotic Lfi system. According to the control criterion, we determine a potential Bautin bifurcation region （denoted by P） of the controlled system. This region contains the Bautin bifurcation region （denoted by Q） of the uncontrolled system as its proper subregion. The controlled system can exhibit Bautin bifurcation in P or its proper subregion provided the control gains are properly chosen. Particularly, we can control the appearance of Bautin bifurcation at any appointed point in the region P. Due to the relationship between Bantin bifurcation and Hopf bifurcation, the control scheme thereby is also viable for controlling the creation and stability of the Hopf bifurcation. In the controller, there are two terms： a linear term and a nonlinear cubic term. We show that the former determines the location of the Hopf bifurcation while the latter regulates its criticality. We also carry out numerical studies, and the simulation results confirm our analyticai predictions.     

周期脉冲作用下Logistic映射的复杂动力学行为及其分岔分析

研究了两种周期脉冲作用下Logistic映射的复杂动力学行为. 随着参数的变化, 该系统产生平衡解、周期解、混沌等现象, 且该系统可经级联倍周期分岔到达混沌. 通过构造Poincaré 映射, 对周期脉冲作用下Logistic映射进行了分岔分析. 最后基于Floquet理论揭示了该系统周期解的分岔机理. 关键词： Logistic映射 脉冲 周期解 分岔机理     

基于状态反馈控制的无线网络拥塞控制流体流模型的Hopf分岔

针对控制无线网络拥塞控制系统中流体流模型的Hopf分岔的问题,提出一种状态反馈控制器.通过选择通信时延作为分岔参数,验证模型在加入状态反馈控制器后,①增加了分岔参数的临界值,扩大了稳定性区域,使系统的Hopf分岔延迟;②通过选择合适的参数,可以容易地改变分岔周期解的稳定性及其分岔方向.理论分析和数据仿真验证了该方法能够有效地控制系统的Hopf分岔.     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

状态反馈控制声光双稳系统的倍周期分岔和混沌

设计了一种动力学状态反馈(DSF)方法控制非线性混沌系统.介绍了DSF方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性.仿真模拟显示,通过选择恰当的控制参数,有效地实现了声光双稳(AOB)系统中倍周期分岔的延迟控制和混沌吸引子中原不稳定周期轨道的稳定控制,同时,还可以将系统控制在2np、3mp 和2np×3mp这样其它任意所需的周期轨道上.     

Control of coexisting attractors via temporal feedback

We propose a method for controlling coexisting attractors in multistable dynamical systems. In this method, the feedback for an initial duration of time can drive the system to the desired state. We have illustrated this method by considering temporal feedback in autonomous as well as non-autonomous dynamical systems. The experimental realisation of the proposed method is also presented.     

Coherent Control of Absorption Resonances via Antirotating Coupling

Effects of the antirotating coupling on the absorption resonances are presented for a microwave driven three-level system. It is shown that nonlinear sideband generation, selective suppression and switching between peaks and dips in the absorption spectrum are obtained as the microwave Rabi frequency is varied. A physical explanation is given in terms of the coherent superposition of an infinite set of transitions that are associated with an infinite set of dressed states, which are created by the rotating and nonrotating couplings as the equivalent bichromatic excitation.